Express your answer as a mixed number simplified to lowest terms. $13\dfrac{2}{19}-7\dfrac{1}{3} = {?}$
Solution: Find a common denominator for the fractions: $= {13\dfrac{6}{57}}-{7\dfrac{19}{57}}$ Convert ${13\dfrac{6}{57}}$ to ${12 + \dfrac{57}{57} + \dfrac{6}{57}}$ So the problem becomes: ${12\dfrac{63}{57}}-{7\dfrac{19}{57}}$ Separate the whole numbers from the fractional parts: $= {12} + {\dfrac{63}{57}} - {7} - {\dfrac{19}{57}}$ Bring the whole numbers together and the fractions together: $= {12} - {7} + {\dfrac{63}{57}} - {\dfrac{19}{57}}$ Subtract the whole numbers: $=5 + {\dfrac{63}{57}} - {\dfrac{19}{57}}$ Subtract the fractions: $= 5+\dfrac{44}{57}$ Combine the whole and fractional parts into a mixed number: $= 5\dfrac{44}{57}$